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Kate and Danny each have $10. Together, they flip a fair coin 5 times.
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Updated on: 17 Feb 2015, 11:34

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E

Difficulty:

55% (hard)

Question Stats:

68%(02:39) correct 32%(02:34) wrong based on 259 sessions

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Kate and Danny each have $10. Together, they flip a fair coin 5 times. Every time the coin lands on heads, Kate gives Danny $1. Every time the coin lands on tails, Danny gives Kate $1. After the five coin flips, what is the probability that Kate has more than $10 but less than $15?

Re: Kate and Danny each have $10. Together, they flip a fair coin 5 times.
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31 Oct 2014, 01:56

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Bunuel wrote:

Tough and Tricky questions: Probability.

Kate and Danny each have $10. Together, they flip a fair coin 5 times. Every time the coin lands on heads, Kate gives Danny $1. Every time the coin lands on tails, Danny gives Kate $1. After the five coin flips, what is the probability that Kate has more than $10 but less than $15?

(A) 5/16 (B) 1/2 (C) 12/30 (D) 15/32 (E) 3/8

total number of possible outcomes when coin will be flipped 5 times= 2^5=32

now, for kate to have more than $10, she must have min. 3 favorable and max. 4 favorable draws in the 5 throws. (because if she wins in all the 5 draws, then she will have $15)

kate will win, every time tails (T) appears on the coin.

case 1) kate wins in 3 draws and losses in two. so we have 3 T's and 2H's(T,T,T,H,H), which can arrange themselves in 5!/(3!)(2!)=10

case 2) kate wins in 4 draws and losses in the 1 draw. so we have 4 T's and 1H (T,T,T,T,H), which can arrange themselves in 5!/4!=5